There’s a simple trick for this problem:

bool IsPowerOfTwo(ulong x)
{
return (x & (x – 1)) == 0;
}
For completeness, zero is not a power of two. If you want to take into account that edge case, here’s how:

bool IsPowerOfTwo(ulong x)
{
return (x != 0) && ((x & (x – 1)) == 0);
}
Explanation

First and foremost the bitwise binary & operator from MSDN definition:

Binary & operators are predefined for the integral types and bool. For integral types, & computes the logical bitwise AND of its operands. For bool operands, & computes the logical AND of its operands; that is, the result is true if and only if both its operands are true.

Now let’s take a look at how this all plays out:

The function returns boolean (true / false) and accepts one incoming parameter of type unsigned long (x, in this case). Let us for the sake of simplicity assume that someone has passed the value 4 and called the function like so:

bool b = IsPowerOfTwo(4)
Now we replace each occurrence of x with 4:

return (4 != 0) && ((4 & (4-1)) == 0);
Well we already know that 4 != 0 evals to true, so far so good. But what about:

((4 & (4-1)) == 0)
This translates to this of course:

((4 & 3) == 0)
But what exactly is 4&3?

The binary representation of 4 is 100 and the binary representation of 3 is 011 (remember the & takes the binary representation of these numbers. So we have:

100 = 4
011 = 3
Imagine these values being stacked up much like elementary addition. The & operator says that if both values are equal to 1 then the result is 1, otherwise it is 0. So 1 & 1 = 1, 1 & 0 = 0, 0 & 0 = 0, and 0 & 1 = 0. So we do the math:

100
011
—-
000
The result is simply 0. So we go back and look at what our return statement now translates to:

return (4 != 0) && ((4 & 3) == 0);
Which translates now to:

return true && (0 == 0);
return true && true;
We all know that true && true is simply true, and this shows that for our example, 4 is a power of 2.

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